Paper 2002/070 Original: eprint.iacr.org/2002/070 ↗

Weak Keys in MST1

Abstract

The public key cryptosystem $MST_1$ has been introduced in~\cite{MaStTr00}. Its security relies on the hardness of factoring with respect to wild logarithmic signatures. To identify `wild-like' logarithmic signatures, the criterion of being totally-non-transversal has been proposed. We give tame totally-non-transversal logarithmic signatures for the alternating and symmetric groups of degree $\ge 5$. Hence, basing a key generation procedure on the assumption that totally-non-transversal logarithmic signatures are `wild like' seems critical. We also discuss the problem of recognizing `weak' totally-non-transversal logarithmic signatures, and demonstrate that another proposed key generation procedure based on permutably transversal logarithmic signatures may produce weak keys.